Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10590338 | C2 | semidirect |
| 3. #10590337 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 5. C3×#4459 | C2 | semidirect |
| 6. C3×#4454 | C2 | semidirect |
| 7. #10589097 | C2 | semidirect |
| 37. #4459 | D3 | semidirect |
| 39. #4454 | D3 | semidirect |
| 114. C3×C3⋊C8 | M16 | semidirect |
| 250. C3⋊C8 | ΓL(1,𝔽25) | semidirect |
| 313. C32 | #1594 | semidirect |
| 365. C3 | #68083 | semidirect |
| 366. C3 | #68163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3714 | 2 |
| #10590338 | 2 |
| #10590337 | 2 |
| #10589325 | 2 |
| C3×#4459 | 2 |
| C3×#4454 | 2 |
| #10589097 | 2 |
| #68163 | 3 |
| #68083 | 3 |